Yes, if the kid is being destructive the sources even say not to ignore that behavior. They also give suggested intervention strategies (though I didn't see a lot of evidence for why they chose those intervention strategies).

And obviously some kids have psychological issues that make all of this meaningless.

I imagine ignoring a bipolar toddler's tantrum is not going to have a meaningful impact. Or at least that is my experience from dealing with bipolar adult tantrums.